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Machine Learning and AI with Simple Python and Matlab Scripts
book

Machine Learning and AI with Simple Python and Matlab Scripts

by M. Umit Uyar
April 2025
Intermediate
384 pages
11h 15m
English
Wiley-IEEE Press
Content preview from Machine Learning and AI with Simple Python and Matlab Scripts

Appendix BSleep Study ANN with Bias

B.1 Inclusion of Bias Term in ANN

Including the bias input into a simple ANN, we have the ANN shown in Figure B.1.

A diagram of a neural network processing inputs for sleep and study hours, with weights W^(1) and biases B^(1). The outputs are combined to predict the final exam grade y^ using the weights W^(2) in the output layer.

Figure B.1 A simple ANN with bias input for sleep‐study example.

A neuron with bias for back propagation is shown in Figure B.2.

upper J equals one half left-parenthesis y minus modifying above y with caret right-parenthesis squared

The partial derivative of upper J with respect to b is

StartLayout 1st Row 1st Column StartFraction partial-differential upper J Over partial-differential b EndFraction 2nd Column equals minus left-parenthesis y minus modifying above y with caret right-parenthesis StartFraction partial-differential modifying above y with caret Over partial-differential b EndFraction equals minus left-parenthesis y minus modifying above y with caret right-parenthesis StartFraction partial-differential modifying above y with caret Over partial-differential e EndFraction StartFraction partial-differential e Over partial-differential b EndFraction period EndLayout

For delta equals minus left-parenthesis y minus modifying above y with caret right-parenthesis f prime left-parenthesis e right-parenthesis, we have

StartLayout 1st Row 1st Column StartFraction partial-differential upper J Over partial-differential b EndFraction 2nd Column equals delta dot 1 equals delta period EndLayout

B.1.1 Inclusion of Bias in Matrices

Suppose there are k different bias values, one for each neuron at layer i with k neurons:

For samples, the dimensions ...

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Publisher Resources

ISBN: 9781394294954